Question: Rewrite as a simplified fraction. ${0.2\overline{81} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 281.8181...\\ 10x &= 2.8181...\end{align*}}$ Subtracting the two equations, we have: ${990x = 279}$ ${x = \dfrac{279}{990}} $ ${x = \dfrac{31}{110}} $